dendrite (mathematics)

In mathematics, a dendrite is a certain type of topological space that may be characterized either as a locally connected dendroid or equivalently as a locally connected continuum that contains no simple closed curves.{{citation

| last = Whyburn | first = Gordon Thomas | authorlink = Gordon Thomas Whyburn

| location = New York

| mr = 0007095

| page = 88

| publisher = American Mathematical Society

| series = American Mathematical Society Colloquium Publications

| title = Analytic Topology

| url = https://books.google.com/books?id=niByQPkPObwC&pg=PA88

| volume = 28

| year = 1942}}.

File:Dendrite julia.png

Importance

Dendrites may be used to model certain types of Julia set.{{citation|title=Complex Dynamics|volume=69|series=Universitext|first1=Lennart|last1=Carleson|author1-link=Lennart Carleson|first2=Theodore W.|last2=Gamelin|publisher=Springer|year=1993|isbn=9780387979427|page=94|url=https://books.google.com/books?id=M-I8qRE8HGUC&pg=PA94}}. For example, if 0 is pre-periodic, but not periodic, under the function $f(z) = z^2 + c$ , then the Julia set of $f$ is a dendrite: connected, without interior.{{citation

| last = Devaney | first = Robert L. | authorlink = Robert L. Devaney

| mr = 1046376

| page = 294

| publisher = Addison-Wesley Publishing Company

| series = Studies in Nonlinearity

| title = An Introduction to Chaotic Dynamical Systems

| year = 1989}}.

dendrite (mathematics)

Importance

References

See also